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Theorem ifpr 3681
 Description: Membership of a conditional operator in an unordered pair. (Contributed by NM, 17-Jun-2007.)
Assertion
Ref Expression
ifpr

Proof of Theorem ifpr
StepHypRef Expression
1 elex 2796 . 2
2 elex 2796 . 2
3 ifcl 3601 . . 3
4 ifeqor 3602 . . . 4
5 elprg 3657 . . . 4
64, 5mpbiri 224 . . 3
73, 6syl 15 . 2
81, 2, 7syl2an 463 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 357   wa 358   wceq 1623   wcel 1684  cvv 2788  cif 3565  cpr 3641 This theorem is referenced by:  suppr  7219  indf  23599  uvcvvcl  27236 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-if 3566  df-sn 3646  df-pr 3647
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